aqueous solution - What determines whether a double displacement reaction will occur?

In normal displacement reactions, reactivity plays a large role and sometimes the reaction doesn't even happen. So is there anything limiting double displacement reactions? For example $\ce{2KI + Pb(NO3)2 -> 2KNO3 + PbI2}$. If reactivity plays a role in this reaction, why does it occur? Isn't the halogen ion (iodide) more reactive than $\ce{NO3-}$?

(I'm a high school chem student so this may come off as a newbie question, sorry)